Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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Calculating circle radius from two points and arc length

For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius. I have 2 way points the ...
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2answers
341 views

Math Puzzle: Area of Concentric Rings

The problem below appeared on the latest round of Google Code Jam: Maria has been hired by the Ghastly Chemicals Junkies (GCJ) company to help them manufacture bullseyes. A bullseye consists of a ...
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191 views

Given a latitude how many miles is the corresponding longitude?

OK so lines of longitude (the distance/circumference around the earth horizontally) differ based on what latitude you are at (0 at north and south poles up to ~25k at the equator.) So given a ...
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1answer
246 views

Bounds of double integral given a circle and a line

Calculate the double integral of the area between the function $$x^2+y^2=25$$ and the line $$y=-x+5$$ in the first quadrant. Now, I am unsure how to choose the bounds for y, I understand that the ...
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1answer
101 views

Calculate points(x, y) within an arc

I am trying to draw lines from the center of a circle to points (x, y) in the circumference. To calculate this the angle is used. I need to render points in between two angles. E.g. Angle 0 to angle ...
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1answer
96 views

Calculating circle properties.

How can I incrementally calculate the angle from angle 0 and the point (x, y) in a circumference path if I have the center of the circle coordinates and the radius of the circle. I have 127 segments ...
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1answer
121 views

Similarity of triangles in a circle

The problem: c is a circle with a diameter AB. t is the tangent at the point B. Now C and D are two points on t and at different sides of B. I draw the line segments AC and AD, the point where AC ...
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2answers
130 views

Circle problem. Finding the length of a segment in the circle.

Here is a picture of the problem. Note that $M$ is the midpoint of $OB$. How do I figure out what $MH$ is? Original image here
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1answer
166 views

One circle, two lines Apollonius' problem

I've been trying to solve special case of Apollonius' problem, where instead of 3 circles i have 1 circle and 2 lines. Acording to: ...
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4answers
6k views

Finding the equation of a circle and a tangent line to the circle given two end points

Given the endpoints $(11, 23)$ and $(6, 13)$ of a circle, find the equation of the circle and the equation of a line tangent to the circle. First, I found the center using the midpoint formula: ...
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1answer
364 views

Point on circumference a given distance from another point

I am writing a game and need to figure out some math. If I have a circle with the equation $r^2 = (x-d)^2+(y-e)^2$, where $r$, $d$, and $e$ are constants, and a point $A(a,b)$, how do I find the ...
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3answers
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Center of Mass of a Circle

How would one find the center of mass of a circle? The center of mass of a rod is given by: $$\frac{1}{M}\int^{L}_{0}\rho x dx$$ So, for a sphere, it would be an area integral, such as: ...
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1answer
104 views

Calculating mean velocity of an orbiting body as it moves towards a point.

I'm making a game, in the game planets orbit a central point in circular orbits, they move directly towards their targets and the vector is simply added to their orbital path. Whilst not realistic it ...
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2answers
584 views

How to calculate angles required to lay out flat pieces in a circle

I want to construct a wheel made of flat pieces of wood, something like this picture: I am unsure how to calculate the difference in angle between each of the flat pieces of wood that make up the ...
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1answer
44 views

Bisectors of angles of circle

Bisectors of angles $A$, $B$ and $C$ of a triangle $ABC$ intersect its circumcircle at $D$, $E$ and $F$ respectively. Prove that the angles of the triangle $DEF$ are $90^{\circ}-\frac{1}{2}A$, ...
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1answer
597 views

How to determine if two points lie in a particular section of circle.

I'll take assistance from the figure below. O is the center of the circle, and A,B,C are the points on the circle, and are known. i.e. the x,y coordinates of these three points are known. I want to ...
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1answer
166 views

How do we know $\pi$ is a constant? [duplicate]

How did the ancient Greeks discover that the ratio of a circle's circumference to its diameter is constant? It does not seem so intuitive. Thanks!
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2answers
209 views

Diameter of a circle with 3 coordinates

The question is: A circle has the points $A=(6,-1)$ $B=(10,-3)$ and $C=(-2,-9)$ on its circumference. A diameter of the circle is drawn which is parallel to BC. How far apart are the two parallel ...
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1answer
299 views

Find a formula for a vector field with given properties

This is the exercise: Give a formula $$F = M(x, y) i+N(x, y)j$$ for the vector fIeld in the plane that has the properties that $$F = 0$$ at $(0,0)$ and that at any other point $(a,b)$, $F$ is tangent ...
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1answer
537 views

when we have circle in hyperbolic plane,what is the center and radius of this circle in Euclidean plane?

Let C be the hyperbolic circle with center Xi, where x>0 and radius r>0. Find the center and radius of this Euclidean circle.
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1answer
74 views

What is the maximum number of circles in proximity to a given point.

The title maybe a bit obscure so I'll try my best to explain the problem here. Below is the Picture that I'll take help from. Say I have a circle A of Radius R ...
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1answer
114 views

What is the official proof (if there is any) for the area of a circle of radius 'r'?

What is the official proof (if there is any) for the area of a circle of radius 'r' ? I remember in my school days they simply told that area of a circle of radius 'r' is $\pi*r^{2}$. The teacher ...
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1answer
404 views

Math - 11th Grade Geometry - Locus

I have a test tomorrow and this might be a question on it. I do not know the answer and I have no idea how I would draw it out if I had to. The question is... Describe the locus of the centers of all ...
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2answers
268 views

Euclidean Geometry Area Problem

Let $\Gamma $ be the circumcircle of triangle $ABC$. Let $A_0$ be the center of the circle lying outside of $\triangle ABC$ and which is tangent to the segment $BC$ and to rays $\overrightarrow{AB}$ ...
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1answer
90 views

Form a Circle with Circles

I need to form a perfect circle out of circles. Given N number of circles each with radius R, how can I find the distance away from the center?
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2answers
146 views

Circumference parametrization

Let $C=\{(x,y)\in \Bbb R^2: (x-x_0)^2+(y-y_0)^2=r^2\}$ and let $\varphi :[0,2\pi]\to \mathbb{R}^2$, $\theta \mapsto (x_o+r\cos \theta, y_0+r\sin \theta)$, with $r>0$. I'm trying to prove that ...
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115 views

Question on inverse trig functions and quadrants? Please Help!

Alright, I was doing a question in a book, and it said: $\displaystyle \cos(2x - \frac{\pi}{6}) = \frac{\sqrt{3}}{2}$ I proceeded and got: $\displaystyle 2x - \frac{\pi}{6} = \frac{\sqrt{3}}{2}.$ I ...
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1answer
135 views

What is the relative behaviour when a center circle surrounded by 6 circles is (recursively) replaced by 6 circles

Start with a given "inner" circle of arbitrary radius (blue) centered at C. Surround it by 6 circles of equal radius. This concerns to known issues of circle packing and is a frequently treated ...
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0answers
123 views

Given 2 outer points of a perfect circle, find the centerpoint

Alright, I hope this makes some sense. I am using a software that can create arcs. This arc is defined by: Begin point End point Center of "circle" The center is supposed to be the center of the ...
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2answers
39 views

Finding the intersctions of two given curves

Given $$ \begin{align} r &= -2\sin(\theta) &&(i)\\ r &= 6\cos(\theta) &&(ii) \end{align} $$ I'm trying to find their intersections. I know $(i)$ is a circle with radius $1$ ...
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1answer
62 views

Problem of sketching a circle

I've to solve a problem in which I've been given this equation: $x^2 + y^2 = 4$ and I've to sketch a circle which is the locus of the equation. Here $2$ is the radius $r$ of the circle. $2$ doesn't ...
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3answers
196 views

Prove that the two line<->circle intersecting points multiplied by eachother are equal to the square of the circle's tangent

On my current math assignment there is a question as follows: Prove the following: A line $k$ through point $P$ intersects a circle in the points $A$ and $B$. Another line $l$ also through $P$ is ...
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1answer
264 views

Maximum number of points a minimum distance apart in a semicircle of certain radius

You have a circle of certain radius $r$. I want to put a number of points in either of the semicircles. However, no two point can be closer than $r$. The points can be put anywhere inside the ...
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3answers
691 views

Intersection of chord with circle knowing the length and a point

Let's take a circle with radius R, and center in O (0, 0). We take on this circle a point A with coordinates xA and yA. We know that point A is one of the endings of a chord with length l. Which is ...
2
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1answer
458 views

Finding side and angle of isosceles triangle inside two circles

I'm having a problem that I'm not sure how to solve (or if it's even possible). It's not homework, just something I'm struggling with for a project. :) Basically, there are two circles, represented ...
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1answer
118 views

Finding the incircle of a circle sector

I'm not great at mathematics so I'm sure this is trivial to most. I have been searching around however and not been able to find how to figure out the incircle of a circle sector, or, in other words, ...
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1answer
92 views

Tangents to Circle

Find the equation of the tangent at the point (acosØ,asinØ) on the circle x^2+y^2=a^2. Tangents are drawn from the point (2a,2a) to the above circle. If the coordinates of the point of contact be ...
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1answer
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Radius of an arch given length and Area of sector

the lengh of an arc of a circle is 12cm.the corresponding sector area is 108cm^2 Find the radius of the circle.
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2answers
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Calculating the coordinates of a point on a circles circumference from the radius, an origin and the arc between the points

We have a circle with the known radius $r$ and the circumference $2\pi r$, and we know a point $P_1$ somewhere on it's circumference. Now, we want to get the coordinates $[x_{P_2},y_{P_2}]$ of the ...
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3answers
86 views

Circle- basic question [closed]

I know this is a basic question, but if I have a circle with radius 2 and I look at the area on the circle between angles $-\pi$ and $\pi$, will that be the bottom half of the circle?
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2answers
156 views

Apollonius circle

I'm given two points, $A$ and $B$, and two lengths, $b$ and $c$. I need to find the locus of point $C$ such that $BC:AC=b:c$. This link describes Apollonius circle of first type, but I can't seem to ...
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3answers
129 views

How many circles fit in the same two dimensional orbit?

I'm trying to figure out how many circles/planets can fit in the same two dimensional orbit. All of the planets and orbits are perfect circles but the planets size and amount can vary. This is for ...
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1answer
102 views

Tangent to circle

The circle $x^2+y^2-4y+3=0$ passes through the points $(0,1),(-\frac{24}{25},\frac{43}{25}),(1,2)$. Its Centre is $(0,2)$ and its radius is $1$. I am asked to find the tangent to the circle through ...
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3answers
61 views

Why exactly is π(mean of radius)² less than the mean of the areas calculated for each radius?

For example, a uniformly distributed value for a radius between 0 and 1 is calculated many times and the area for each radius is calculated: ...
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4answers
555 views

Circle/Triangle math problem

The question asks to find angles $\angle X$ and $\angle Y$, however I don't know how to do this without assuming that lines $\overline {GO}$ and $\overline{OJ}$ are parallel. The only angle given is ...
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2answers
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Calculating a circles radius from two known points on its circumference

For a simulation, I need to be able to calculate the radius $r$ of a circle $C$, knowing only two points on its circumference, $P_1$ and $P_2$, as well as the distance between them ($a$) and how much ...
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2answers
394 views

6 point lying on a common circle

$Z$ is an interior point of segment $XY$. Three semicircles are drawn over segments $XY$, $XZ$ and $ZY$ on the same side. The midpoints of the arcs are $M1$, $M2$ and $M3$ respectively. A circle ...
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1answer
3k views

How to find the central angle of a circle?

My book states the following: Likewise, we can take a circular cone with base radius $r$ and slant height $l$, cut it along the dashed line in Figure 2: and flatten it to form a sector ...
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1answer
47 views

How do you calculate the velocity of the pencil?

I'm drawing a quarter circle with a pencil on a sheet of graph paper. The radius is 10cm. At a given moment in time the velocity at which I am moving the pencil is 5cm/s (centimeters per second). I ...
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1answer
266 views

Calculate vector position

I'm trying to calculate & move vertices to their average "radius" and form a circle from these new positions. Example: I have 8 vertices selected, I have a little script in Maya that will iterate ...